56.4.54 problem 51

Internal problem ID [8943]
Book : Own collection of miscellaneous problems
Section : section 4.0
Problem number : 51
Date solved : Monday, January 27, 2025 at 05:20:31 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }-9 x y^{\prime }+25 y&=0 \end{align*}

Using series method with expansion around

\begin{align*} 0 \end{align*}

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 19

Order:=6; 
dsolve(x^2*diff(y(x), x$2)-9*x*diff(y(x), x)+25*y(x) = 0,y(x),type='series',x=0);
 

\[ y = x^{5} \left (c_{2} \ln \left (x \right )+c_{1} \right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 18

AsymptoticDSolveValue[x^2*D[y[x],{x,2}]-9*x*D[y[x],x]+25*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_1 x^5+c_2 x^5 \log (x) \]